About Optics & Photonics TopicsOSA Publishing developed the Optics and Photonics Topics to help organize its diverse content more accurately by topic area. This topic browser contains over 2400 terms and is organized in a three-level hierarchy. Read more.

Topics can be refined further in the search results. The Topic facet will reveal the high-level topics associated with the articles returned in the search results.

Abstract

We discuss the feasibility of a quantum nondemolition measurement (QND) of photon number based on cross phase modulation due to the Kerr effect in photonic crystal waveguides (PCW’s). In particular, we derive the equations for two modes propagating in PCW’s and their coupling by a third order nonlinearity. The reduced group velocity and small cross-sectional area of the PCW lead to an enhancement of the interaction relative to bulk materials. We show that in principle, such experiments may be feasible with current photonic technologies, although they are limited by material properties. Our analysis of the propagation equations is sufficiently general to be applicable to the study of soliton formation, all-optical switching and can be extended to processes involving other orders of the nonlinearity.

Figures (3)

Top left: waveguide mode dispersions calculated by the 3D Finite Difference Time Domain (FDTD) method. The solid (black) line is the light line in the photonic crystal, above which modes are not confined by total internal reflection.Top right: group velocities of the two modes derived from the disperion curves by numerical differentiation (vg=dωdk). Bottom left: modes of the PhC lattice at the k=πa point. The mode with even vertical symmetry relative to the waveguide axis corresponds to the red dispersion curve and the odd symmetry mode is that of the blue dispersion curve. Bottom right: A scanning electron micrograph of a fabricated PCW in AlGaAs.

Phase shift due to a single signal photon with a lifetime of 200 ps, after propagation through a 100 μm AlGaAs waveguide with a narrow probe and no group velocity mismatch (A), and the energy required for an external pulse to obtain a SNR of 1 (B). In (A) and (B) it is assumed that the signal and probe are at 1500 nm and two-photon absorption is not present. In (C) we plot the phase for the case of the signal photon in waveguide 1 at 1550 nm and probe at 1620 nm in waveguide 0. The required probe energy for this scheme is shown in (D). In all plots, the blue and red curves correspond to both the signal and the probe in waveguide modes 0 or 1. The black curve corresponds to the probe and signal in different waveguide modes

Tables (1)

Table 1. values for coupling γ for different modes of the waveguide in units of a-2, and mode volumes for each unit cell of the waveguide (in units of a-3. 1 and 2 refer to the first and second modes of the waveguide.

Metrics

Table 1.

values for coupling γ for different modes of the waveguide in units of a-2, and mode volumes for each unit cell of the waveguide (in units of a-3. 1 and 2 refer to the first and second modes of the waveguide.